Question

Consider the following hypotheses: H0: mean = 5 H1: mean < 5 A test is performed with a sample of size 25. The sample mean was 4.73 and the population standard deviation is 1.2. Assume that the population is approximately normal. Use the TI-84 PLUS calculator to compute the P-value. Round your answer to four decimal places (for example: 0.0138). Write only a number as your answer.

Answer 1

Answer:

0.1406.

Step-by-step explanation:

Given : $H_o:\mu = 5$

           $H_1:\mu < 5$  

To Find : compute the P-value.

Solution:

Sample size = 25

n < 30

So, we will go for t-test

Now we are given that  the population standard deviation is 1.2.

$\sqrt{\frac{s}{n}}=1.2$ Where s is the variance

$\sqrt{\frac{s}{25}}=1.2$

$\sqrt{s}=6$

$s = 6^2$

$s = 36$

So, the variance is 36

we require sample standard deviation for t test

So, Sample standard deviation = $\sqrt{\frac{s}{n-1}}$

                                                  = $\sqrt{\frac{36}{25-1}}$

                                                  = $1.2247$

Formula of t-test = $\frac{m-\mu}{\frac{s}{\sqrt{n}}}$

Where s is the standard deviation of sample

Sample mean = 4.73

Mean = $\mu = 5$

s = 1.2247

n =25

So,  $t=\frac{5-4.73}{\frac{1.2247}{\sqrt{25}}}$

$t=1.1023$

So, p value with respect to t-table is 0.1406.

Hence p-value is  0.1406.